7^{x+1}=3^{x+2}

Lösung

7^{x + 1} = 3^{x + 2}

x = \frac{2 ln ( 3 ) - ln ( 7 )}{ln ( 7 ) - ln ( 3 )}

Dezimale

x = 0.29660 \dots

Schritte zur Lösung

7^{x + 1} = 3^{x + 2}

Wende Exponentenregel an

(x + 1) ln (7) = (x + 2) ln (3)

Löse

(x + 1) ln (7) = (x + 2) ln (3) : x = \frac{2 ln ( 3 ) - ln ( 7 )}{ln ( 7 ) - ln ( 3 )}

x = \frac{2 ln ( 3 ) - ln ( 7 )}{ln ( 7 ) - ln ( 3 )}

4^{x} = 8^{x + 1}

5^{x^{2}} = 2 5^{4 - x}

3^{x + 1} = 3^{5}

3^{2 x - 1} = 81

128 = \frac{5 ^{2 n - 5}}{2 ^{4 n}}